Finite Group Databasebeta

← #20252766

Subgroups — #20252766

Order 6016.

704 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 704 conjugacy classes of subgroups — too many to draw. Only its 145 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689959C211yesmaximal, characteristic
2C2×#13094055C212yesmaximal, complemented
3#15689305C214yesmaximal, complemented
4#15689300C214yesmaximal, complemented
5#15689141C212yesmaximal, complemented
6#15689107C211yesmaximal, characteristic, complemented
7C47×#536C211yesmaximal, characteristic, complemented
8#13094072C2212yes—
9#13094071—22no—
10#13094070—22no—
11#13094069—22no—
12#13094069C2212yes—
13C2×#10625350—22no—
14C2×#10625350C2212yes—
15#41×D47—24no—
16#13094055—24no—
17#13094055C2218yescomplemented
18C2×#10625337—22no—
19C2×#10625336—22no—
20C2×#10625329C2212yescomplemented
21#13093952C2218yescomplemented
22#13093943C2212yescomplemented
23#13093941C2212yescomplemented
24C2×#41×C47C2211yescharacteristic
25C22×Q8×C47C2211yescharacteristic, complemented
26C4⋊Q8×C47C2212yescomplemented
27#124×C47C2212yescomplemented
28#123×C47—22no—
29C22⋊Q8×C47—22no—
30#117×C47C2211yescharacteristic, complemented
31#41×C47—22no—
32#41×C47—22no—
33C2×Q8×C47—21no—
34C2×Q8×C47—22no—
35C2×Q8×C47—22no—
36C2×Q8×C47C2312yes—
37C2×Q8×C47C2311yescharacteristic
38C2×D4×C47D412yes—
39C2×D4×C47C2311yescharacteristic
40C22×C4×C47—21no—
41C22×C4×C47D412yes—
42C22×C4×C47C2311yescharacteristic
43C2×C22⋊D47—24no—
44C2×C22⋊D47—22no—
45#10625354—24no—
46Q8×D47—24no—
47#10625352—28no—
48#10625352—24no—
49D4×D47—28no—
50D4×D47—24no—
51#10625350—24no—
52#10625350—24no—
53#10625350—22no—
54#10625350—24no—
55#10625350—22no—
56#10625350D414yes—
57#10625350C2314yes—
58C2×D188—22no—
59C2×D188D412yes—
60C2×C4×D47—24no—
61C2×C4×D47—22no—
62C2×Dic94—22no—
63C2×Dic94D412yes—
64C4⋊C4×C47—21no—
65C4⋊C4×C47—24no—
66C22⋊C4×C47—21no—
67C22⋊C4×C47—24no—
68C42×C47C2312yes—
69#10625337—28no—
70#10625336—28no—
71#10625329—22no—
72#10625329C2314yes—
73C2×C47⋊C8—22no—
74C23×C47C2×D412yes—
75C23×C47C2×D411yescharacteristic
76C22×D47—24no—
77C22×D47—22no—
78Q8×C47—22no—
79Q8×C47—24no—
80Q8×C47—41no—
81Q8×C47—41no—
82D4×C47—24no—
83D4×C47—22no—
84C2×C4×C47—22no—
85C2×C4×C47—22no—
86C2×C4×C47—22no—
87C2×C4×C47—22no—
88C2×C4×C47—42no—
89C2×C4×C47C2×D412yes—
90C2×C4×C47C2×D412yes—
91C2×C4×C47C2×D412yes—
92C2×C4×C47C2×D411yescharacteristic
93C2×C4×C47C2411yescharacteristic
94C22⋊D47—28no—
95C22⋊D47—24no—
96C22⋊D47—24no—
97C2×Dic47—24no—
98C2×Dic47—22no—
99D188—24no—
100D188—22no—
101D188C2×D414yes—
102C4×D47—28no—
103C4×D47—24no—
104C4×D47—24no—
105Dic94—24no—
106Dic94—22no—
107Dic94C2×D414yes—
108C47⋊C8—24no—
109C22×C47—22no—
110C22×C47—41no—
111C22×C47—42no—
112C22×C47#12012yes—
113C22×C47C22×D411yescharacteristic
114C2×D47—24no—
115C2×D47—82no—
116C2×D47—84no—
117C4×C47—22no—
118C4×C47—42no—
119C4×C47—42no—
120C4×C47#12011yescharacteristic
121C4×C47#12011yescharacteristic
122C4×C47C22×D412yes—
123Dic47—24no—
124#3022—471nomaximal, Sylow
125C2×C47—21no—
126C2×C47—22no—
127C2×C47—42no—
128C2×C47C2×#12011yescharacteristic
129D47—44no—
130#585—471no—
131C2×#137—472no—
132#536D4711yescharacteristic, complemented
133#456—474no—
134#455—474no—
135#421—472no—
136#413—471no—
137C47#302211yescharacteristic, complemented, Sylow
1382−1+4—472no—
1392−1+4—942no—
140H(5,𝔽2)—472no—
141H(5,𝔽2)—942no—
142H(5,𝔽2)—942no—
143C2×#41—472no—
144C2×#41—944no—
145C2×#41—942no—
146C2×#41C2×D4711yescharacteristic
147C22×Q8C2×D4711yescharacteristic, complemented
148#137—478no—
149#137—944no—
150C2×Q16—942no—
151C2×SD16—942no—
152C2×M16—472no—
153C4⋊Q8C2×D4712yescomplemented
154#124C2×D4712yescomplemented
155#123—22no—
156C22⋊Q8—22no—
157#117C2×D4711yescharacteristic, complemented
158#104—478no—
159#101—472no—
160#100—472no—
161#41—22no—
162#41—22no—
163#41—474no—
164#41—474no—
165#41—944no—
166#41—944no—
167#41—944no—
168#41—948no—
169#41—944no—
170#41—942no—
171#41—942no—
172#41—944no—
173C2×Q8—21no—
174C2×Q8—22no—
175C2×Q8—22no—
176C2×Q8—472no—
177C2×Q8—942no—
178C2×Q8—944no—
179C2×Q8C22×D4712yes—
180C2×Q8C22×D4711yescharacteristic
181C2×D4—472no—
182C2×D4—942no—
183C2×D4—944no—
184C2×D4—948no—
185C2×D4—942no—
186C2×D4—944no—
187C2×D4C22⋊D4712yes—
188C2×D4C22×D4711yescharacteristic
189C22×C4—21no—
190C22×C4—944no—
191C22×C4—942no—
192C22×C4C22⋊D4712yes—
193C22×C4C22×D4711yescharacteristic
194Q16—948no—
195SD16—948no—
196M16—474no—
197M16—942no—
198C2×C8—942no—
199C4⋊C4—21no—
200C4⋊C4—24no—
201C22⋊C4—21no—
202C22⋊C4—24no—
203C42C22×D4712yes—
204C23—944no—
205C23—942no—
206C23C2×C22⋊D4712yes—
207C23C2×C22⋊D4711yescharacteristic
208Q8—22no—
209Q8—24no—
210Q8—41no—
211Q8—41no—
212Q8—474no—
213Q8—944no—
214Q8—942no—
215D4—24no—
216D4—22no—
217D4—474no—
218D4—944no—
219D4—948no—
220D4—944no—
221D4—944no—
222D4—942no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—22no—
227C2×C4—42no—
228C2×C4—948no—
229C2×C4—944no—
230C2×C4—942no—
231C2×C4—944no—
232C2×C4—944no—
233C2×C4D4×D4712yes—
234C2×C4D4×D4712yes—
235C2×C4C2×C22⋊D4712yes—
236C2×C4C2×C22⋊D4711yescharacteristic
237C2×C4C23×D4711yescharacteristic
238C8—944no—
239C22—22no—
240C22—41no—
241C22—42no—
242C22—944no—
243C22—3762no—
244C22—3764no—
245C22#1309399212yes—
246C22C22×C22⋊D4711yescharacteristic
247C4—22no—
248C4—42no—
249C4—42no—
250C4—944no—
251C4#1309399211yescharacteristic
252C4#1309399211yescharacteristic
253C4C2×D4×D4712yes—
254C2—21no—
255C2—22no—
256C2—42no—
257C2—1884no—
258C2C2×#1309399211yescharacteristic
subgroupG/H
centerC2C2×#13093992
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#536C2
socleC2×C47C2×#120
hypercenter#536D47
hypocenterC47#3022
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C22×C4 ◁ #536

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×#13094055C2semidirect
3. #15689305C2semidirect
4. #15689300C2semidirect
5. #15689141C2semidirect
6. #15689107C2semidirect
7. C47×#536C2semidirect
17. #13094055C22semidirect
20. C2×#10625329C22semidirect
21. #13093952C22semidirect
22. #13093943C22semidirect
23. #13093941C22semidirect
25. C22×Q8×C47C22semidirect
26. C4⋊Q8×C47C22semidirect
27. #124×C47C22semidirect
30. #117×C47C22semidirect
132. #536D47semidirect
137. C47#3022semidirect
147. C22×Q8C2×D47semidirect
153. C4⋊Q8C2×D47semidirect
154. #124C2×D47semidirect
157. #117C2×D47semidirect